Erik measures a cone with a radius of 12 feet and a height that is half the length of the radius. What is the volume of Erik’s cone? Use 3.14 for pi and express your answer to the nearest tenth of a cubic foot.(1 point)

The volume of Erik’s cone is cubic feet.

1 answer

To find the volume of a cone, we use the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

Given:

  • Radius \( r = 12 \) feet
  • Height \( h = \frac{1}{2} \times r = \frac{1}{2} \times 12 = 6 \) feet

Now substituting the radius and height into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times (12^2) \times 6 \]

Calculating \( 12^2 \):

\[ 12^2 = 144 \]

Now substituting that back into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times 144 \times 6 \]

Calculating \( 144 \times 6 \):

\[ 144 \times 6 = 864 \]

Now substituting that in:

\[ V = \frac{1}{3} \times 3.14 \times 864 \]

Calculating \( 3.14 \times 864 \):

\[ 3.14 \times 864 = 2716.16 \]

Finally, dividing by 3:

\[ V = \frac{2716.16}{3} \approx 905.38666667 \]

Rounding to the nearest tenth:

\[ V \approx 905.4 \]

Thus, the volume of Erik’s cone is approximately 905.4 cubic feet.